Saibal writes:
> Yes, this is inherent in the construction of the CSO. s(t) has to be
> smaller than 1 for any finite t. But what about transfinite values for t?
> Since transfinite numbers can be described in a mathematical consistent way,
> it is possible to define a mathematical model of the CSO surviving beyond
> s(t) = 1 . Following Tegmark one should thus believe that the CSO will
> experience this moment.
I had made a similar point in my message at
http://www.escribe.com/science/theory/m2178.html. The way I posed the
question was, can you have a universe with two subsystems, such that one
sees the other do an infinite amount of computation? This gets away
from what I see as arbitrary assumptions about which one's measure of
time is "correct". I agree that the question relates to the existence
of transfinites, and that this fits better into Tegmark's approach than
Schmidhuber's. Even in a UTM universe though we could postulate a TM
which executes an infinite number of steps.
Hal
Received on Fri Oct 13 2000 - 14:55:35 PDT